# Some fundamental properties on the sampling free nabla Laplace transform

## TL;DR

This paper explores fundamental properties of the sampling-free nabla Laplace transform, enhancing its theoretical framework and practical utility in discrete fractional order systems.

## Contribution

It introduces 14 new theorems and consolidates existing properties, advancing the theoretical understanding of the nabla Laplace transform in fractional systems.

## Key findings

- 14 lemmas on existing properties
- 14 theorems on innovative features
- Enhanced effectiveness of N-transform

## Abstract

Discrete fractional order systems have attracted more and more attention in recent years. Nabla Laplace transform is an important tool to deal with the problem of nabla discrete fractional order systems, but there is still much room for its development. In this paper, 14 lemmas are listed to conclude the existing properties and 14 theorems are developed to describe the innovative features. On one hand, these properties make the N-transform more effective and efficient. On the other hand, they enrich the discrete fractional order system theory